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Elliptic Curve Playground

Explore a Weierstrass curve over ℚ. Invariants and rational-point checks use exact arithmetic; the real plot is a numerical view.

01 / Curve

Enter rational coefficients for y² + a1xy + a3y = x³ + a2x² + a4x + a6.

02 / Real locus

Plot points are approximate. Exact rational points appear below.

03 / Check a point

04 / Find rational points

Search reduced x = p/q with |p| ≤ the numerator bound and 1 ≤ q ≤ the denominator bound. For each x, both rational y values are checked exactly. This is a bounded search, not a complete point list.